Molecular Simulations of Tilted Chain Crystal - Amorphous Interfaces in Polymers
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METHODOLOGY Figure 1 shows a schematic diagram of the interphase with the three chain populations illustrated. The polymers are modeled as chains of united atoms with fixed bond length (1.53 A) and bond angle (1120). The interphase is modeled as a monoclinic box with top and bottom face corresponding to crystal lamellae. The interaction between united atoms was taken to be a truncated Lennard-Jones Potential with a =3.94 A and "/k= 49.3 K, typical of CH 2 qroups. The reference unit cell was taken as orthorhombic with a = 7.94 A, b = 3.54 A, c = 2.53 A, typical of polyethylene. Periodic boundary conditions are imposed in x and y directions. Total number of chains taken were 23 with 10 as the number of tails. The z-thickness of the box was 45 A. A Monte Carlo simulation in the NVT ensemble was constructed. Four basic Monte Carlo moves were used to change the local conformation of the chains and topology of the interface. 'End-rotation' move samples configuration space by the simple rotation of one to three atoms at the end of the chain. 'End reptation' removes one atom from the end of a randomly picked tail and appends it on another tail. Concerted rotation algorithm [6] is used for the 'Endbridging' move, where pairs of a bridge and a tail or a loop and a tail are inter-transformed. This introduces changes in topology of the interface and acts as a powerful way to equilibrate the structure. Concerted rotation is also used within the same chain as 'Intra-Chain' move, to remove and re-grow four atoms. An initial configuration was generated starting from an all-trans monoclinic cell. A few atoms were removed to ensure proper density of the amorphous phase sandwiched between two crystals. This was also important to drive the system towards a metastable configuration. This structure is then allowed to equilibrate using the moves described above. Approximately 10 million Monte Carlo moves were performed on one system and about 5000 configurations were collected to obtain the averages. More information about the specific procedure and other details can be obtained elsewhere [7]. Characterization of structure and properties The simulation box was divided into bins, normal to the z-axis and the structural properties were calculated for each bin as described below. These properties were averaged over all the configurations to get the ensemble average. Density - The density represents the ratio of occupied volume fraction in a slice to that in the crystal phase. The atoms were assumed to be hard spheres and their contribution to each bin was assumed proportional to their volume fraction in that particular bin. In the extreme case of hard sphere diameter approaching zero, this will yield the same result as number density. Order - The bond orientation order parameter is defined as S = [(3 - 1)/2], where Sis the angle measured by a C-C-C bond chord with respect to the z-plane. An average is taken over all the chords within the bin for each configuration. The contribution to a particular bin was determined based on the length frac
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